MAYBE

We are left with following problem, upon which TcT provides the
certificate MAYBE.

Strict Trs:
  { a__f(X1, X2) -> f(X1, X2)
  , a__f(g(X), Y) -> a__f(mark(X), f(g(X), Y))
  , mark(g(X)) -> g(mark(X))
  , mark(f(X1, X2)) -> a__f(mark(X1), X2) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

We add following dependency tuples:

Strict DPs:
  { a__f^#(X1, X2) -> c_1()
  , a__f^#(g(X), Y) -> c_2(a__f^#(mark(X), f(g(X), Y)), mark^#(X))
  , mark^#(g(X)) -> c_3(mark^#(X))
  , mark^#(f(X1, X2)) -> c_4(a__f^#(mark(X1), X2), mark^#(X1)) }

and mark the set of starting terms.

We are left with following problem, upon which TcT provides the
certificate MAYBE.

Strict DPs:
  { a__f^#(X1, X2) -> c_1()
  , a__f^#(g(X), Y) -> c_2(a__f^#(mark(X), f(g(X), Y)), mark^#(X))
  , mark^#(g(X)) -> c_3(mark^#(X))
  , mark^#(f(X1, X2)) -> c_4(a__f^#(mark(X1), X2), mark^#(X1)) }
Weak Trs:
  { a__f(X1, X2) -> f(X1, X2)
  , a__f(g(X), Y) -> a__f(mark(X), f(g(X), Y))
  , mark(g(X)) -> g(mark(X))
  , mark(f(X1, X2)) -> a__f(mark(X1), X2) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

We estimate the number of application of {1} by applications of
Pre({1}) = {2,4}. Here rules are labeled as follows:

  DPs:
    { 1: a__f^#(X1, X2) -> c_1()
    , 2: a__f^#(g(X), Y) -> c_2(a__f^#(mark(X), f(g(X), Y)), mark^#(X))
    , 3: mark^#(g(X)) -> c_3(mark^#(X))
    , 4: mark^#(f(X1, X2)) -> c_4(a__f^#(mark(X1), X2), mark^#(X1)) }

We are left with following problem, upon which TcT provides the
certificate MAYBE.

Strict DPs:
  { a__f^#(g(X), Y) -> c_2(a__f^#(mark(X), f(g(X), Y)), mark^#(X))
  , mark^#(g(X)) -> c_3(mark^#(X))
  , mark^#(f(X1, X2)) -> c_4(a__f^#(mark(X1), X2), mark^#(X1)) }
Weak DPs: { a__f^#(X1, X2) -> c_1() }
Weak Trs:
  { a__f(X1, X2) -> f(X1, X2)
  , a__f(g(X), Y) -> a__f(mark(X), f(g(X), Y))
  , mark(g(X)) -> g(mark(X))
  , mark(f(X1, X2)) -> a__f(mark(X1), X2) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

The following weak DPs constitute a sub-graph of the DG that is
closed under successors. The DPs are removed.

{ a__f^#(X1, X2) -> c_1() }

We are left with following problem, upon which TcT provides the
certificate MAYBE.

Strict DPs:
  { a__f^#(g(X), Y) -> c_2(a__f^#(mark(X), f(g(X), Y)), mark^#(X))
  , mark^#(g(X)) -> c_3(mark^#(X))
  , mark^#(f(X1, X2)) -> c_4(a__f^#(mark(X1), X2), mark^#(X1)) }
Weak Trs:
  { a__f(X1, X2) -> f(X1, X2)
  , a__f(g(X), Y) -> a__f(mark(X), f(g(X), Y))
  , mark(g(X)) -> g(mark(X))
  , mark(f(X1, X2)) -> a__f(mark(X1), X2) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

The input cannot be shown compatible

Arrrr..